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Munich Personal RePEc Archive
Exact prediction of inflation in the USA
Ivan, Kitov
IDG RAS
July 2006
Online at https://mpra.ub.uni-muenchen.de/2735/
MPRA Paper No. 2735, posted 15 Apr 2007 UTC
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Exact prediction of inflation in the USA
Ivan O. Kitov
AbstractA linear and lagged relationship between inflation and labor force growth rate has been recently
found for the USA. It accurately describes the period after the late 1950s with linear coefficient 4.0,
intercept -0.03, and the lag of 2 years. The previously reported agreement between observed and
predicted inflation is substantially improved by some simple measures removing the most obvious
errors in the labor force time series. The labor force readings originally obtained from the Bureau of
Labor Statistics (BLS) website are corrected for step-like adjustments. Additionally, a half-year time
shift between the inflation and the annual labor force readings is compensated. GDP deflator
represents the inflation. Linear regression analysis demonstrates that the annual labor force growth
rate used as a predictor explains almost 82% (R2=0.82) of the inflation variations between 1965 and
2002. Moving average technique applied to the annual time series results in a substantial increase in
R2. It grows from 0.87 for two-year wide windows to 0.96 for four-year windows. Regression of
cumulative curves is characterized by R2>0.999. This allows effective replacement of GDP deflation
index by a “labor force growth” index.
The linear and lagged relationship provides a precise forecast at the two-year horizon with
root mean square forecasting error (RMSFE) as low as 0.008 (0.8%) for the entire period between
1965 and 2002. For the last 20 years, RMSFE is only 0.4%. Thus, the forecast methodology
effectively outperforms any other forecasting technique reported in economic and financial literature.
Moreover, further significant improvements in the forecasting accuracy are accessible through
improvements in the labor force measurements in line with the US Census Bureau population
estimates, which are neglected by BLS.
Key words: inflation, labor force, forecast, the USA
JEL Classification: E3, E6, J21
Introduction
It has been found that inflation in the USA and other developed countries is a linear and
potentially lagged function of the growth rate of labor force level (Kitov, 2006a). In the
largest developed economies, this relationship has different coefficients and lags. In Japan,
Germany, the UK, and some other European countries, there is no clear delay between labor
force change and inflation, i.e. the two economic variables evolve synchronously (Kitov,
2006b; 2006d). In the USA and France, however, labor force change leads inflation by two
years (Kitov, 2006d). The two-year lag can be easily obtained from annual readings,
smoothed and cumulative curves of the labor force growth rate and inflation measured in the
countries. Thus, the labor force measurements in the USA and France could be used for
forecasting inflation at a two-year horizon.
The leading role of labor force change observed in the USA and France evidences that
the change is the driving force behind inflation. The smoothed and cumulative curves
obtained for the two variables are in excellent agreement during the period starting in the
early 1960s in both countries. Unfortunately, the agreement deteriorates further in past. Such
degradation is partially induced by a critical reduction in the accuracy of relevant
measurements. Even definitions of labor force and inflation were quite different before the
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1960s, as described in technical documentation provided by the US Bureau of Labor
Statistics (BLS, 2002).
We do not focus here on the uncertainty in the measurements in the 1950s and before.
Instead, our attention is concentrated on the improvement of the US labor force
measurements, which have been carried out during the last forty five years. Raw data
available at the BLS website (http://www.bls.gov) is characterized by a number of
adjustments and revisions, which cannot be treated as appropriate ones in the framework of
the linear relationships between inflation and labor force change rate. Therefore, an
assessment of the artificial spikes forced by BLS in the raw data is fulfilled and some
corrections are carried out for obtaining a more consistent time series.
The corrections applied to the labor force readings have a great impact on the
performance of the linear relationship. This paper documents progressive improvements in
standard statistical estimates of the relationship with increasing accuracy of the labor force
measurements. In addition, predictive power of the relationship is assessed for various
periods, as routinely used in the forecasting literature.
There are just few papers devoted to inflation description and prediction we refer to.
Reasons for that are obvious. Inflation models include autoregression as an almost inevitable
component. The relationship under study includes no past or future inflation values, no
variable representing real economic activity such as unemployment or output gap, and no
monetary or financial parameters such as M3 aggregate and interest rates. Instead, the
relationship relates inflation to only the change in the number of people who have an
intention to obtain a paid job or its equivalent. Hence, there is almost nothing inherited by the
relationship from the mainstream economic, econometric, and monetary models of inflation.
Results of the study are presented in six sections. First section briefly describes the
concept of the labor force induced inflation and empirical coefficients obtained for the USA.
GDP deflator is used as a measure of inflation. The deflator is considered as the most robust
and accurate variable representing inflation as a real phenomenon because of its inherent
relation to the entire economy. An implicit but principal assumption of the concept under
development is that all economy-wide variables are related to population-wide quantitative
characteristics including entire labor force. Hence, such measures of inflation as CPI and
CPE are not appropriate because of their limited population relevance. The variables
represent some population sub-ensembles not population as a whole. In statistical physics or
thermodynamics, fluctuations in such sub-ensembles are not representative on the entire
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ensemble level. Following this observation, we do not consider CPI and CPE in the study as
potentially misleading variables.
Second section details the adjustments applied by the US BLS to the raw labor force
measurements for the period starting from 1960 (BLS, 2006). Several step adjustments of the
labor force level introduced by BLS in the annual readings are smoothed. A simple procedure
is applied - the step adjustments are distributed proportionally over previous years depending
on the period when the changes were accumulated.
Section 3 elaborates on the BLS adjustment applied in 1996 to the labor force readings
between January 1990 and December 1993. A “regular” correction applied to the annual
values does not help in this case. The 1990 difference between the observed and predicted
inflation values is so large that it substantially biases overall statistics. To reveal the reason
for the discrepancy the Census Bureau measurements of civilian population (CP) are used. A
prominent spike in the civilian nonistitutional population (CNP) increment is reported by
BLS for 1990. The spike is not supported by the CB population estimates for the same year.
The increment values in both time series are in a good agreement, however, during the entire
period between 1980 and 2000 except 1990. The spike is also removed from the original data
to fit the postcensal measurements of civilian population. Usage of the intercensal population
estimates might provide further improvements in the CNP estimates made by BLS.
Linear regression analysis in Section 4 provides quantitative estimates for the
agreement between the observed and predicted inflation values. The labor force readings are
used as a predictor. A number of corrections of the labor force estimates is fulfilled and
corresponding improvements in the regression results are reported. The original labor force
readings for the period between 1965 and 2002 provide a benchmark. The interval selected
allows avoiding effects of the labor force data with high uncertainty before 1960 and those of
the data after 2002, which are prone to further revisions. In the benchmark case, R2=0.62 and
standard deviation is 1.5%. The best corrected labor force time series provides an increase in
R2 up to 0.89 and decrease in standard deviation to 0.8%. Further improvements are feasible
if to refine the historical labor force data in line with the CB population estimates and to
revise the CPS procedures.
Section 5 presents the results of the regression analysis in terms of forecasting.
Prediction is a straightforward application of the relationship between inflation and labor
force change, at least in the USA. The two-year lag provides a powerful tool for the inflation
forecast at the two-year horizon with no extra efforts as compared to the regression. The
inflation prediction is intrinsically an out-of-sample one because it uses only past values of
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labor force. For the entire period between 1965 and 2002, root mean square forecast error
(RMSFE) at an annual rate is only 0.8%. Hence, the relationship outperforms modern
inflation forecasting models, at least those reported in the literature.
Because of severe problems related to a “break” in the inflation time series around
1984, it becomes a standard way to present forecasting results separately for the periods
before and after the break. Our model has no “break” problems due to an outstanding
accuracy in the description of the period between 1970 and 1990. The accuracy is a natural
consequence of the existence of the objective link between labor force and inflation. Despite
the excellent agreement over the entire period between 1965 and 2002, forecasts for two sub-
periods, before and after 1984, are also presented to facilitate comparison to other forecasts.
Section 6 concludes and discusses empirical and theoretical advantages of the linear
relationship between labor force change and inflation. Empirically, the relationship
establishes a strong trade-off between the variables removing any potential discrepancy
during measurements. Theoretically, the relationship represents a natural extension of the
economic framework, which has been developed by Kitov (2005a; 2005b; 2006a-2006d).
The framework links such principal economic variables as GDP, personal income
distribution, and now inflation and unemployment to only one endogenous parameter –
population. Population counting gives an exact natural number and, thus, provides exact
values for the economic parameters.
1. The relationship between inflation and labor force change
The empirical relationship used in the study is obtained and validated by data measured in
the USA and Japan (Kitov, 2006a; 2006b). It links together inflation, unemployment, and
labor force change rate. An implicit assumption of the model is that inflation and
unemployment do not depend directly on real economic growth (Kitov, 2006c).
As defined by the model (Kitov 2006a), inflation and unemployment are linear and
potentially lagged functions of labor force change as expressed by the following
relationships:
�(t)=A1dLF(t-t1)/LF(t-t1)+A2 (1)
U(t)=B1dLF(t-t2)/LF(t-t2)+B2 (2)
where �(t) is the inflation rate at time t, U(t) is the unemployment rate at time t, LF(t) is the
labor force level, t1 and t2 are the time lags between the inflation, unemployment and the
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labor force, respectively, A1, B1, A2, and B2 are country-dependent empirical coefficients of
the linear functions. The coefficients may vary through time for a given country as various
measures (definitions) of the studied variables are introduced (Kitov, 2006d).
Linear relationships (1) and (2) define inflation and unemployment separately as
functions of labor force change. These two variables are indivisible sides of a unique process,
however. The process is the labor force growth, which is accommodated in real economies
though two channels. The first channel is an increase in employment and corresponding
change in personal income distribution (PID). All persons obtaining new paid jobs or their
equivalents presumably change their incomes to some higher levels. There is an ultimate
empirical fact, however, that the US PID does not change with time in relative terms (Kitov,
2005b). The increasing number of people at higher income levels, as related to the new paid
jobs, leads to a certain disturbance in the PID. This over-concentration must be compensated
by such an extension in the income scale, which returns the PID to its original density. The
income scale stretching is called inflation (Kitov, 2006a). The mechanism responsible for the
compensation and the scale stretching has some relaxation time, which effectively separates
in time the source of inflation, i.e. the labor force change, and the reaction, i.e. inflation itself.
The second channel is related to those who failed to obtain a new paid job, i.e. to
enter the employment. These people do not leave the labor force but enter unemployment.
Effectively, they do not change the PID because they do not change their incomes. So, the
total labor force change equals the unemployment change plus employment change, the latter
process to be easily expressed through inflation. In the case of a "natural" behavior of an
economic system, proportion between unemployment and inflation is retained through time
and the linear relationships hold separately. There is always a possibility, however, to fix one
of the two variables. For example, central banks are able to fix inflation by some monetary
means. Such a violation of the natural behavior will undoubtedly distort the partition of the
labor force change – the portion previously accommodated by inflation will be redirected to
unemployment. To account for this effect one should to use a generalized relationship as
represented by the sum of relationships (1) and (2):
�(t)+U(t)= A1dLF(t-t1)/LF(t-t1) +B1dLF(t-t2)/LF(t-t2)+A2+B2 (3)
Equation (3) balances labor force change, inflation and unemployment, the latter two
variables potentially lagging by different times behind the labor force change. The
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importance of this generalized relationship is demonstrated in (Kitov, 2006d), where the case
of France before and after joining the European Monetary Union is analyzed.
For the USA, there is no need so far to apply relationship (3) because corresponding
monetary policies do not change the natural partition of labor force change, as observed since
the late 1950s. For the USA, A1=4, A2=-0.03, t1=2 years (GDP deflator as a measure of
inflation), B1=2.1, B2=-0.023, t2=5 years. Figure 1 compares observed and predicted inflation
(annual and cumulative values) as obtained for the USA by Kitov (2006a).
Negative constant A2 makes a permanent increase in labor force of great importance for
avoiding deflationary periods. Population growth rate of 0.01 to 0.015 per year, as observed
in the USA during the last twenty years, completely compensates the effects of the negative
term A2. With the boomers' retirement, however, the labor force growth rate will decelerate
starting from 2005.
For Japan, A1=1.77, A2=-0.003, t1=0 years (GDP deflator as a measure of inflation)
(Kitov, 2006b). The labor force change rate measured in Japan is negative since 1999 and
corresponding measures of inflation, GDP deflator and CPI, are negative as well. There is no
indication of any recovery into the positive zone any time soon if to consider the decrease in
working age population and participation rate as observed from 1999.
The relationship demonstrates an excellent performance over time and countries. At the
same time, there was no formal statistical assessment done for the relationship in the
previous papers. Therefore, the relationship is statistically assessed below in order to
demonstrate the improvements obtained when the largest errors are removed from to the
labor force time series. The errors are discussed in the next two sections.
2. The labor force measurements and adjustments
Results of the labor force measurements are published at a monthly basis by the US Bureau
of Labor Statistics (BLS). The readings are obtained during the monthly Current Population
Surveys (CPS) conducted for BLS by the US Census Bureau (CB). Details of the CPS
definitions, methods and procedures are presented in technical documentation (CB, 2002a;
2002b). Briefly, about 60,000 scientifically selected households compile a sample
representing civilian non-institutional population as a whole and are surveyed every month at
a rotational basis. All interviewed persons above 15 years of age have to answer a number of
questions related to their current labor status. The labor status is one of the following three:
in the labor force, i.e. employed or unemployed (not employed but available for a paid job
immediately), not in the labor force. Figures in given age-sex-race groups obtained in a
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survey and corrected for the number of non-interviewed due to various reasons are projected
to the entire population using some specific weights related to so-called population controls.
The weights reflect the fact that the distribution of the population selected for the sample
may differ from that for the population as a whole.
Therefore, the labor force readings obtained in the CPS are characterized by two
intrinsic types of uncertainty related to the measurements of the labor force and the total
population estimates/counts, respectively. Labor force, as an economic variable, has a long
history of changes in definitions, estimation procedures and methodology as documented in
(BLS, 2003; 2006).
The CB population estimates used by BLS also undergo some adjustments and
revisions between decennial censuses according to new information about birth and death
rates and international migration. Decennial censuses in the USA reveal large “errors of
closure” (CB, 2002a), i.e. the discrepancy between the estimated and the census counted
population. The errors are age-sex-race dependent and are as large as several per cent. For
example, the undercount of the population between 25 years and 34 years of age reached
5.92% in the 2000 census, i.e. instead of the estimated 39.9 million 43.2 million was counted.
Thus, when using the population controls in the labor force estimation procedure, one has to
bear in mind that the population controls are exposed to multiple revisions and modifications
in line with new enumeration and other estimates.
The changes in labor force concepts, definitions and methods induce uncontrollable
(but, hopefully, not large) errors in the labor force estimates made in the USA during the last
50 years. Not every change in the CPS questionnaires and practice of the CPS can be
extrapolated back in past because of the absence of relevant information. In addition to these
immeasurable changes, there are adjustments which are applied to the labor force time series
and can be described quantitatively.
Figure 2 summarizes the changes in the labor force level during the last 45 years. In
1962, the labor force was decreased by 200,000 according to the population data obtained in
the 1960 census. Here we first meet an example of the labor force level adjustment. Despite
an obvious cumulative character of the population estimate error, the adjustment is applied to
only one year, i.e. in a way, which artificially introduces a step in the labor force level. The
US Census Bureau proportionally distributes the error of closure over the ten years preceding
the censuses (CB, 2002a). The population controls used in the estimation of the labor force
are adjusted by BLS impulsively, however.
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In 1972, an adjustment related to the 1970 census was introduced and the total
population was increased by about 800,000. The labor force level was increased by only
300,000, however, that corresponds to different labor force participation rates characterizing
different age-sex-race groups used in the surveys.
An important modification was introduced in 1974. The CNP has been estimated by an
“inflation-deflation” method since then. BLS states that the modification had no impact on
the labor force level, however, in contrast to the next year when about 76,000 refugees
arrived from Vietnam. The labor force was also increased. This is an example of a real step
change in the labor force level. The newcomers entered the labor force at once. No correction
for this event is made in the labor force estimates.
In January 1978, a 250,000 increase in the labor force was introduced as resulted from
an expansion of the survey sample (the number of the sample areas was increased from 461
to 614) and revisions of the estimation procedure. A series of changes in methods and
procedures between 1979 and 1985 did not result in any important revision of the labor force
level. In 1985, “the population controls used in the second-stage ratio adjustment method
were revised” (BLS, 2006) that led to an about 350,000 increase in the labor force.
Almost the largest labor force positive revision was implemented in 1994. The CNP for
1990 was increased by 1,100,000, the employment level by 880,000, and the unemployment
by 175,000. This adjustment was related to the 1990 census and distributed by BLS over the
period from January 1990 to December 1993. The labor force level was revised up by about
1,000,000 in January 1990, however, introducing a very high step in the time series.
In 1997, the labor force level was increased by 320,000 due to the new population
controls related to the demographic updates for the number of international migrants. New
composite estimation procedures introduced in 1998 resulted in lower estimates of the
civilian labor force. It is not clear what effect it had on the years before 1997, but in 1997 the
labor force was reduced by 229,000. A minor positive labor force change of 60,000
introduced in 1999 was related to updates of immigration information.
Since 2000, several major changes have been introduced into the CPS. The changes
reflect results of the 2000 census enumeration, introduced by a 1,600,000 positive labor force
level correction, and a higher population growth rate between 2000 and 2003, additional
900,000 were distributed month by month between January 2000 and December 2002. Total
increase accumulated in 2000 reached 1,900,000. An upward adjustment by 614,000 was
introduced into the labor force in January 2003.
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In January 2004, the labor force was decreased by 440,000, however, to reflect new
immigration estimates for the period between 2000 and 2004. So, frequency and amplitude of
the adjustments has been progressively increasing in the twenty first century as presented in
Figure 2. During the 1960s and 1970s, there were only minor and seldom changes.
The detailed description of the BLS revisions evidences that the reasons behind the
adjustments are clear and valid. At the same time, except the case of the Vietnamese
refugees, the labor force level errors compensated by the adjustments were accumulated
during periods longer than one year. This makes the step adjustments to introduce some
additional errors in the labor force estimates. The errors are especially important to
understand and remove in the following regression analysis because the step level
adjustments create spikes in corresponding growth rates as the first differences, which
substantially affect results of such a least squares based procedure as linear regression.
There are two simple ways to reduce the influence of the step adjustments. The first is
to subtract the adjustments from the official estimates. This would remove the artificial steps
from the time series. This approach has a substantial deficiency, however. It contradicts the
observations: both the census enumerations of the total population and in population
subgroups. Also it excludes advances in the labor force measurement procedures which
reduce uncertainty in the readings.
Another way is to distribute the step adjustments over corresponding periods. For
example, the adjustments associated with decennial censuses were apparently accumulated
during the entire period between corresponding censuses. The proportional distribution
applied by the Census Bureau to the civilian population estimates would be a reasonable first
approximation. One should bear in mind, however, that actual distribution over years differs
from its simplest representation and some years between censuses are potentially
characterized by higher or lower than average changes. Therefore, using the proportional
distribution one may reduce variation in the labor force measurements but can not recover the
actual pattern.
Figure 3 illustrates the proportionally distributed corrections designed to smoothing the
BLS step adjustments. The corrections effectively reduce variance in the labor force
increment values as Figure 4 demonstrates. There is one year, however, which does not show
any improvement. It deserves a special consideration.
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3. The problem of 1990
In the previous Section, we corrected the labor force estimates for the step revisions. The
revisions are recognized by BLS as leading to the noncomparability of labor force levels
(BLS, 2006). So, the steps are artificial and our corrections resulted in several improvements
expressed in the smoothness of the modified labor force change rate curve compared to the
original one, especially between 1970 and 1990.
There is a significant outlier, however, in 1993. The predicted inflation still falls to
negative values and differs from the observed value by almost 3.5%. This discrepancy is of
critical importance for the linear relationship between inflation and labor force change. It is
clear that the larger is the difference the lower is the confidence that the relationship is valid:
large changes are usually better measured in relative terms and provide major input into
statistics of fit. If large changes are not well described by a model, common sense and
statistics both evidence the failure of the underlying concept. Due to the importance of the
1993 outlier for the concept, we study this case in more detail.
First, I requested BLS to give an explanation of the sudden drop in the labor force
change rate observed in 1991. In a personal communication, explanation just referred to a
recession observed between July 1990 and March 1991. Supposedly, the recession led to a
decrease in the employment growth rate and corresponding drop in the observed labor force
change rate. If the explanation is valid, it denies the approach because the reason or driving
force behind inflation is not the labor force change but business cycles.
The revisions for the years between 1990 and 1994 are well documented by BLS
(2003, 2006). There was only one step adjustment applied in 1990, when the labor force was
increased by 1,055,000. The step increase was accounted for in the previous Section but the
correction did not give any significant improvement. In any case, there is no inconsistency in
the revisions from the BLS side. But it is only one side of the story.
BLS borrows its population control numbers from the Census Bureau and uses them
in somewhat independent way. To obtain the labor force estimates, BLS multiplies civilian
noninstitutional population by participation rate. The latter value is obtained through the
monthly CPSs and characterized by a relatively high accuracy. At least the participation rate
values are consistent through time. The CNP is an estimated (enumerated) parameter,
however. The largest revisions are usually applied after decennial censuses. The closest
census to 1991 was in 1990. So, a hypothesis easily arises that BLS used some earlier and
inaccurate revisions to the population controls, which later were improved by the Census
Bureau.
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The Census Bureau provides two sets of population estimates for the period after
1990. The first estimate of civilian population is obtained between censuses and is called a
postcensal estimate. This estimate uses all available contemporaneous information to assess
population changes induced by births, deaths, and net migration. The second estimate is
based on enumerated values obtained in censuses and is called an intercensal estimate for
years between the two censuses. The second estimate is characterized by a superior accuracy
because it is based on actually counted numbers.
Both population estimates were obtained from the CB website. There is a principal
difference between the CNP used by BLS for the population controls and the civilian
population presented by CB. But the latter represents a good approximation of the former if
to consider annual increments not levels. Figure 5 displays the annual increments in the BLS
CNP and increments in the civilian population of 16 years of age and over as obtained from
the post- and intercensal estimates. All the curves practically coincide between 1980 and
1989 with just minor deviations of the CNP increments from those of the civilian population.
The latter is the same for the post and intercensal estimates. In 1990, a spike is observed in
the BLS CNP which is demonstrated neither by the intercensal nor by the postcensal civilian
population estimates. This spike actually represents the BLS step adjustment applied to the
CNP in 1990. The increments in the postcensal estimates practically coincided with those in
CNP for the rest of the years. Hence, the postcensal estimates is probably the source of
information for the CNP estimates conducted by BLS. The intercensal estimates demonstrate
consistently higher annual increments resulted from a number of revisions conducted by the
Census Bureau after the 2000 census. The revisions compensate for the “error of closure".
Hence, the sudden drop in the labor force change rate in 1991 is induced by the
1,000,000 overestimate in the CNP increase during 1990. If the participation rate is
determined accurately (~66%), the labor force estimate for 1990 is positively biased above its
actual value and the estimate for 1991 is not biased. As a result, the difference between the
1991 and 1990 labor force estimates is below its actual value by approximately 660,000. One
can use the intercensal civilian population curve for a better estimate of the labor force
change in 1990 and 1991. The curve definitely shows that the annual increment values grew
gradually between 1990 and 1992.
One can apply the CB estimates of civilian noninstitutional population increment for
the entire period after 1990 instead of those used by BLS. It is a sophisticated procedure,
however, which includes re-estimation of participation rates in numerous age-sex-race
groups and we leave this problem with BLS. For the purposes of our study, we just distribute
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the excess of 660,000 over the period between 1990 and 1992, as the CB intercensal estimate
shows. Figure 6 illustrates the smoothness of the obtained distribution of the labor force
increment between 1985 and 2000 compared to that for the original distribution. There is no
deep trough near 1990 any more.
4. Regression
In hard sciences, statistical estimates usually do not provide additional confidence in results
if some curves literally coincide as the cumulative curves in Figure 1. Formally, one can
apply some statistical techniques in order to assess the residual level of uncertainty related to
the curves. The reason for the statistical estimates of uncertainty is not to report them as they
are but to develop some instrumental and/or theoretical approach to decrease the attained
level of uncertainty. This is a standard procedure in hard sciences: to measure – to estimate
degree of uncertainty – to develop a new approach to improve accuracy of the measurements,
instrumentally or theoretically – to measure at the new level of accuracy, which can
potentially distinguish between accepting and denying the model. An implicit assumption
behind the procedure is that real empirical relationships can be potentially evaluated with a
progressively lower level of uncertainty improving our understanding of real processes
behind the relationships. (We do not consider here the uncertainty principle, which limits
accuracy of simultaneous measurements of some quantum variables.) Levels of uncertainty
related to such physical relationships are usually estimated as the discrepancy between
predicted and observed values. This approach often makes any additional statistical estimates
unnecessary. A researcher has usually a good reason to relate the observed discrepancy to
corresponding measurement errors if the observations and predictions do not violate physical
laws.
In economics, the feedback between measurement accuracy and theoretical analysis is
much weaker. There are few recommendations on the level of measurement accuracy
necessary to resolve specific economic problems in a majority of economic papers. Even
those devoted to measurement accuracy usually do not link the evaluated level of uncertainty
to solution of principal economic problem. Accuracy problems are left to measuring agencies
with no specific criticism of the applied definitions, procedures, practices, etc.
Replacing the improvements in measurement accuracy as an ultimate demand of
evolving economic theory, statistical analysis becomes a backbone of economics as a
science. Such an approach is considered as an appropriate one because of a strong and
consolidated opinion among economists that real economy is a stochastic and unpredictable
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process. Thus, only statistics is able to provide an adequate formal description of economic
processes. In other words, there are no other links between economic variables except
statistical ones. Because of the absence of predetermined and unambiguous links between
economic variables, there is no specific need to improve accuracy of economic
measurements. One can not distinguish between random errors in the measurements and
random behaviour of economic variables. Statistically, they maybe treated as identical. As a
result, standards of economic measurements are driven not by demands of science itself but
by internal conventions developed in measuring agencies and funding. The latter is always a
critical issue, but in the absence of reliable objective relationships between economic
variables, there is no rule how to distinguish the most important measurements for the overall
progress of economic theory.
I am also sure that real economy is a stochastic process. But not an unpredictable one!
Driving forces behind numerous economic variables – this is the real source of stochastic
behaviour. The driving forces are governed by a large number of natural processes and
events, which effectively introduce a stochastic component into the forces. However, many
macroeconomic variables are completely defined by the forces with some time lags providing
a better opportunity to reveal the forces and to predict the variables.
For example, inflation is completely controlled by relative growth in labor force, as
claimed in this paper. Relationship between the variables is linear and lagged. Thus, inflation
is a random variable to the extent the labor force growth is random. Labor force change rate
depends on a variety of financial, fiscal, social, demographic, climatic, and historical
processes. But labor force level can be measured with any desirable accuracy if a strict
definition is given. Thus, the aim of this Section is to demonstrate that inflation can be also
predicted exactly with improvements in the accuracy of labor force measurements.
As statistical inferences play an important role in the current economic thinking it
would be reasonable to provide some results of a standard regression analysis. This allows
translation of the findings into “econometric language” for better understanding of the link
between labor force and inflation. Regression analysis does not make the findings about the
link more convincing by itself, with the most actual future problem being a substantial
improvement in the accuracy of the labor force measurements.
Inflation is chosen as a dependent variable and labor force change rate is the
predictor. The period between 1965 and 2002 is selected for balancing between sample
length and uncertainty in corresponding measurements in the USA. Before 1965, the large
variations in the labor force annual increment (see Figure 1) evidence some measurement
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problems. After 2002, the labor force measurements are prone to further (and potentially
severe) revisions, i.e. any regression results would be just temporary. So, the length of the
period is 37 years with 38 annual readings. Such a choice does not indicate that we consider
the studied relationship as not working before 1965. It should be valid before 1965, to some
point in the past which practically can not be determined due to data related problems. After
2002, the relationship is also valid and will be valid before economic behavior of the US
population and institutions changes in some dramatic way.
The annual readings of inflation are regressed against the predicted values of inflation
as obtained using relationship (1) with the coefficients described in the text and in Kitov
(2006a) and the measured rates of the labor force change. Table 1 lists some principal results
of the regression. The regression coefficient is 0.763 (0.099) and R2=0.62. Thus, about 60%
of the inflation variability is explained by the linear relationship. Here we have to mention
that the labor force readings are shifted by two years ahead to compensate for the observed
time lag. Standard error of the prediction with the linear lagged relationship is 0.015 (1.5%).
P-value and t-statistic associated with the regression coefficient are given for additional
confidence.
As discussed in Kitov (2006a) and above, the labor force measurements are
characterized by a significant scatter. The relatively low R2 obtained in this first regression
experiment indicates that almost 40% of the labor force variance is potentially related to the
measurement error with the residual 60% explaining the variance of the inflation. As found
in Sections 2 and 3, the original labor force readings are strongly biased by the step
adjustments carried out by BLS. The reason why we have smoothed the original data and
introduced a special correction to the 1990 reading is to make the measured values closer to
actual or exact ones. Whether the goal is achieved may be demonstrated by a comparison of
the results of regression analysis using the original BLS labor force readings to those
obtained with the corrected values. Table 1 answers the question quantitatively. The
regression coefficient for the corrected labor force readings for the same period is 0.890
(0.085) with R2 =0.75. This result evidences a significant improvement in the explanation of
the inflation variation by the labor force change rate if the latter is just corrected for the
simplest and obvious errors introduced by BLS. Apparently, the original labor force
measurements include some more errors associated with changes in definitions, procedures,
practices, etc. These errors are poorer described and understood, but a scrupulous researcher
might reach better regression results conditional on time and efforts invested. We do not go
further in our efforts to recovering unbiased signals from the original data.
15
Another significant improvement can be achieved by a trivial time shift of the labor
force estimates by half a year. As discussed in Kitov (2006a), the labor force annual readings
are obtained by a weighted averaging of monthly measurements with corresponding seasonal
adjustment. Obviously, these average values are closer to the midyear monthly estimates than
to the end-of-year monthly values. Therefore, the annual readings are expected to better
describe the July through June changes in the labor force rather than the January through
December changes. The easiest way to compensate for the time shift between the inflation
and labor force measurements is to recalculate the average values for the corresponding
shifted periods with December in the middle, i.e. July through June of the next year. Table 1
provides the results of the regression analysis as obtained for the newly averaged labor force
values marked as “July-June dLF/LF”. For the original data series, i.e. the one not corrected
for the step adjustments, R2 increases from 0.62 to 0.73, and standard deviation decreases
from 0.015 to 0.013. Thus, there is a difference in the explanatory power between the
original and half-year shifted data series. The latter is superior. There is also a lesson for
researchers using original economic data sets. Sometimes even a half-year shift results in
further improvements in statistical description.
A different way to achieve a half-a-year shift in the labor force series is the averaging
of two neighboring annual values. This procedure effectively makes the center of the two-
year wide periods, i.e. December, to represent the averaged readings and introduces
additional noise suppression. Table 1 lists regression results for two cases: the half-year shift
applied to the original time series “dLF/LF+1/2 year shifted LF” and the shift applied to the
corrected values “dLF/LF (corrected)+1/2 year shifted LF”. (Further in the text, “1/2 year
shift” means averaging of two neighboring values.) In both cases, the dependent variable is
the annual inflation. R2
increases to 0.807 and 0.845, and standard deviation decreases to
0.011 and 0.010, respectively. Figure 7 displays the observed inflation values and those
predicted with the corrected and shifted labor force estimates. In fact, there is almost nothing
left to explain with the annual readings considering the noisy measurements of the labor
force and potential measurement errors in the GDP deflator values.
Smoothing by moving average is a simple and effective way to suppress random noise
by destructive interference. Efficiency of such a method when applied to the labor force and
inflation measurements was demonstrated by Kitov (2006a). Seven-year moving average
provided an outstanding similarity of the smoothed curves - observed and predicted ones. In
this paper, a shorter time series is analyzed with only 38 observations. This makes the seven-
year window too wide compared to the total length.
16
At first, averaging by two-, three-, and four-year wide moving windows was carried out
using the corrected labor force annual readings. Then the “1/2 year shift” procedure was
applied to the averaged values, i.e. an additional weighted averaging. Then the annual
inflation readings were regressed against the predicted values. Table 1 summarizes
corresponding information. Averaging in two-year wide moving windows with one year step
provides a better description of the annual inflation readings (R2=0.866) compared to that
obtained using the corrected labor force values (R2=0.752) and the half-year shifted original
values (R2=0.807). Standard deviation is only 0.009 (0.9%), i.e. potentially less than the
accuracy associated with the inflation measurements. However, the best result is achieved by
the three-year window averaging with R2=0.894 and standard deviation of 0.008. The
extension of the moving window to four years provides additional improvement neither in
R2=0.893 nor in standard error – 0.008. Such a result is not an unexpected one because of the
two-year lag between the inflation and labor force change. Labor force readings around the
defining year may introduce some noise suppression due to effects of serial correlation
intrinsic to the labor force measurements but do not bring any actual information in addition
to that already available for the defining year. When extended beyond some critical width,
the averaging window includes more and more information related to different years, what is
pure noise for the defining year. As a result, correlation between the inflation and the labor
force deteriorates.
The regression of the observed and predicted values of inflation averaged in two-,
three-, and four-year wide windows with one-year step provides an additional improvement.
Table 1 evidences that corresponding R2 values are consequently increasing: 0.897, 0.941,
and 0.963. One can consider the improvements as an indication of the expected noise
suppression. Figure 8 depicts the predicted and observed curves for the latter case with the
error in 1990 intentionally left to demonstrate its influence on the deviation of the predicted
curve.
The last two rows in Table 1 are devoted to the cumulative curves. In practice, the
curves obtained by a progressive summation of the inflation values, the measured and
predicted ones, starting from 1965 (and 1963 for the predicted series) are just routinely
constructed indices. The curves look identical with just minor deviations induced by such
errors as we discussed for the 1990 civilian noninstitutional population value. Regression
confirms the visual identity. R2 reaches 0.999 for the GDP deflator and 0.998 for CPI
inflation. Standard deviation is 0.014 and 0.026, respectively.
17
5. Forecasting inflation
Forecasting inflation is the principal task for monetary authorities. In developed countries,
there are several approaches elaborated during the last half-century. It would be not an
exaggeration to divide bankers and economists involved in the forecasting process into two
principal groups, as introduced by Mankiw (2005), “technical” forecasters and “scientific”
ones. There is no any unique concept or approach recognized as a superior one across the
groups and inside the groups as well. In practice, technical decisions (or “engineering” in the
Mankiw’s classification) are more popular than scientific ones. (Here I would like to notice
that no engineering is possible without science.) This slight superiority is not justified by any
better result in forecasting relative that obtained by the scientific community. The superiority
is dictated by an easier access to monetary power (Mankiw, 2005) and consideration of the
fact that somebody has to make principal decisions in the situation of the absence of any hard
science. The relationship between inflation and labor force provides all necessary means for
precise forecasts with potential improvement depending on accuracy of labor force
measurements.
To some extent, current inflation forecasting for monetary purposes can be described as
a common sense selecting between the tools available and experiences. That is why personal
influence is so important in actual practice of monetary authority - there is no best
description of inflation processes - just numerous competing. Moreover, as stated in the
modern literature on inflation forecasting- Stock&Watson (1999; 2005), Atkeson&Ohanian
(2001); Canova (2002), Hubrich (2003), Ang, Bakaert, and Wei (2006), among others, a
naïve approach based on the assumption that tomorrow’s inflation will be equal to the one
observed today is superior during the last twenty years to almost any scientific approach
based on information related to previous behavior of inflation and other economic and
financial variables. In fact, those approaches, which are superior to the naïve one, are very
close to it and often are volatile ones. They will probably loose their predictive power soon
(Stock&Watson, 2005). Hence, to be a great forecaster one needs only to know current
inflation value and maybe have some historical experience to be ready for a “pivot point”
when inflation will start to deviate from its current “moderate” behavior.
There is no strict scientific knowledge behind these “engineered” forecasts, however.
This makes long-run forecasts to be very poor, as it was observed during the 1970s and
1980s. Both naïve and “engineered” approaches failed to explain sudden peaks and
disinflation. There is no simple candidate parameter, except inflation itself used in the naïve
18
or autoregressive form, which could potentially explain historical readings of inflation
through time and countries. Many parameters provide temporary and country specific
improvements over the AR-type models, however.
The approach we present resolves these problems. It does not use autoregressive
properties of inflation, i.e. there is no rational expectation implied, perfect or imperfect one,
what is a common feature for the Phillips curve based models (Rudd&Whelan, 2005). It
covers the entire period when relatively accurate labor force data is available for developed
countries (Kitov, 2006b; 2006d).
One can describe inflation in the USA with an uncertainty controlled by the accuracy of
the labor force survey, as demonstrated in Section 4. Thus, a direct way to improve the
current predictive power of the inflation/labor force relationship is available. Only some
simple arrangements are necessary. Moreover, one can easily introduce a target value for the
inflation uncertainty and link it to the resources available and needed.
According to our concept, inflation forecasting is equivalent to the inflation regression
carried out in the previous Section. Standard deviation listed for various regressions is, by
definition, the prediction uncertainty for the entire period between 1965 and 2002. In
forecasting practice, standard deviation is called root mean square forecast error (RMSFE).
This term indicates that forecasted values of inflation are obtained in the framework of out-
of-sample approach, i.e. using only past values of predictors. Models explaining inflation,
such as the family of Phillips curves, often include past, contemporaneous, and future values
of economic parameters (for example, Gali, Gertler, and Lopez-Salido (2001) and Sbordone
(2002)) .
The best prediction for the annual readings with RMSFE of 0.008 (0.8%) is obtained in
Section 4 using a three-year moving average. Even the annual readings of the labor force
with the simplest improvements such as smoothing of the step adjustments and a half-year
shift provide RMSFE of 0.096 (0.96%). These values are lower than any RMSFE at the two-
year horizon I was able to find in literature for the same or comparable period.
It is practically a standard to make forecasts for periods before and after 1983
separately. To match this standard, the period between 1965 and 2003 was split at the same
point. Linear regression is carried out for the separate periods and RMSFE (standard
deviations) are computed. Table 2 lists the obtained statistical estimates. The best prediction
for the earlier period is characterized by RMSFE=0.011and R2=0.81. It is received using the
three-year moving average. Standard deviation of the inflation time series for the same period
19
is 0.023 (first row in Table 2). For the period between 1983 and 2002, the bets prediction is
also obtained with the three-year moving average: RMSFE=0.0045 and R2=0.72. Standard
deviation for the inflation during this period is 0.009. Stock and Watson (2005) provide a
comprehensive list of RMSFE for the periods between 1970 and 1984 and between 1984 and
2004. For the first period, the best RMSFE=1.85%, and for the second – 0.67%.
Our forecasts are made on an annual rate of inflation and at the two-year horizon. In
the literature, a quarterly basis is more popular for various reasons. There is only a marginal
difference between statistical estimates made for the inflation at an annual and quarterly basis
for the period between 1965 and 2002: mean value is 0.042 and 0.041, standard deviation is
0.024 and 0.025, respectively. For the two periods before and after 1983, the difference
between the values obtained for the annual and quarterly readings is also of 0.001, i.e.
practically negligible.
In addition to the overall statistics, linear regression analysis was carried out at a
quarterly rate for the period between 1965Q1 and 2002Q1. Predicted values were obtained by
relationship (1) using the annual labor force measurements two years before the predicted
quarter, i.e. the average labor force over the four preceding quarters. For the entire period
between 1965Q1 and 2002Q1, R2=0.64 and stdev=0.015, i.e. very close to the values
obtained at an annual rate for the annual readings of labor force without any correction:
R2=0.62 and stdev=0.015. This indicates that the quarterly forecasts from literature and our
annual forecasts can be compared without any adjustment. The comparison undoubtedly
evidences that predictive power of the relationship between inflation and labor force is
superior to any other reported forecasting methodology. Moreover, the relationship is the
same for both periods. Values of linear coefficient (4) and intercept (-0.03) are obtained from
the entire period between 1965 and 2002. There is no additional adjustment applied to the
coefficients when forecasting inflation for a specific time span. In different forecasting
models, coefficients, the number of which is usually more than 2, are adjusted to the periods
before and after 1983 in order to minimize RMSFE. Even using these additional advantages
the models fail to produce a good prediction compared to that the relationship between
inflation and labor force easily provides.
6. Discussion and conclusions
The most important conclusion is that inflation can be described (predicted) with a high
accuracy, being at the same time a stochastic variable. In the framework of the linear lagged
relationship between inflation and labor force change, there is no difference between
20
description and forecast because only past values of labor force are used. Further
improvements in the accuracy of inflation forecasts are straightforward and depend only on
our capabilities to measure labor force level. Stochastic properties of inflation are entirely
defined by those of the labor force. Therefore, inflation as a process is stochastic to the extent
the labor force growth is stochastic. If labor force could be controlled by some means,
inflation would be also controllable.
Current methods applied by the Federal Reserve Board do not provide any
contemporaneous influence on the inflation and potentially affect only the future evolution of
the variable to the extent they affect the labor force. Moreover, one can conclude that there
has been no change in the methods, at least since the late 1950s, which has affected the
observed evolution of inflation, i.e. its link to the labor force change rate. The evolution of
the labor force has been affected by different processes, not by the FRB actions, during the
period. One can hardly imagine any influence of FOMC decisions on working age
population growth rate.
The standard errors of inflation forecast (or RMSFE) obtained using three-year moving
averages apparently are the best ones available so far and are superior to any other prediction
at the two-year horizon including the Phillips curve, interest rate, monetary aggregates, and
survey forecasts. The simplest and obvious corrections applied to the labor force readings
resulted in the R2 increase by 0.25-0.40. In addition, the best standard error of prediction has
approached 0.8%. Revisions of the labor force estimates through the last forty to fifty years
in line with the CB civilian population re-estimates is a natural next step. There should be no
artificial steps in the labor force estimates potentially induced by changing definitions and
procedures and the population controls should reflect the last revisions made by the CB.
Noise suppression by moving average results in a significant increase of R2 to the level
approaching 1.0. The predicted and observed curves are hardly distinguishable when four-
year wide moving windows are used. The cumulative curves (or indices) could successfully
substitute each other over the entire period with R2=0.9991.
There is a number of negative conclusions one can make considering the results of the
analysis. The Phillips curve was not mentioned in the text in any positive sense because it
obviously does not exist. There is a link between inflation and unemployment as described
by relationship (3), but unemployment or any other variable expressing real economic
activity does not affect inflation in the Phillips curve sense. This is not rational expectation,
supply shock and real economic activity what determines evolution of inflation. These
variables potentially have some marginal effect on the labor force evolution observed in the
21
USA during the last 50 years. So, I would consider the Phillips curve as a dead end in
macroeconomic theory.
There is no structural or any other kind “break” around 1984. The changes in the
inflation behaviour observed in the 1970s and 1980s are a pure consequence of the
accelerated labor force growth associated with the measured participation rate increase
(Kitov, 2006a). There were two distinct phases in the participation rate increase separated by
a short period of “quietness”. When reached its peak value around 1983, the participation
rate effectively stalled at the attained level and has not been changing since then. As a
consequence, the labor force has been growing only due to the growth in working age
population. This period is known as “Great Moderation” and was possible completely due to
the constant participation rate and population growth at an annual rate above 1.0% since
1983.
The “Great Moderation” is currently approaching its natural end. The labor force
projections made by various institutions (CBO, 2004; BLS, 2005) undoubtedly indicate a
decrease in the participation rate and a decaying growth rate of the working age population.
According to the projections, staring from 2010, the annual increase in labor force will be
less than 1,200,000 – the value separating inflation and deflation. Hence, a deflationary
period is very probable starting 2012 because of the two-year lag between the labor force
change and inflation. Similar prediction was given by Kitov (2006a) based on a projection of
working age population in the USA.
Figure 9 details the prediction based on the CBO’s projection of the labor force.
Currently (2006) inflation undergoes a short-term increase with a peak in 2007 reaching
3.2%. After 2007, a gradual decrease will be observed with the first red figure in 2012.
22
References
Ang, A., Bakaert, G. and M. Wei, (2006). “ Do macro variables, asset markets, or
surveys forecast inflation better?”, FRB Working Paper ?
Atkeson, A., Ohanian, L.E., (2001). “Are Phillips curves useful for forecasting
inflation?”, Federal Reserve Bank of Minneapolis Quarterly Review 25, 2-11.
Bureau of Labor Statistics, (2003). “Revisions in the CPS effective January 2003”,
http://www.bls.gov/cps/rvcps03.pdf
Bureau of Labor Statistics, (2005). “Labor force projections to 2014: retiring boomers”,
Monthly Labor Review, November 2005.
Bureau of Labor Statistics, (2006). “Employment and Earnings. Household data”,
http://www.bls.gov/cps/eetech_methods.pdf
Canova, F., (2002). “G-7 inflation forecast”, EBC Working Paper No 151.
Congressional Budget Office, (2004). “CBO’s Projections of the labor force”,
September 2004.
Census Bureau, (2002a). “ Methodology: national intercensal population estimates",
http://www.census.gov/popest/archives/methodology/intercensal_nat_ meth.pdf
Census Bureau, (2002b). “The Current Population Survey: Design and Methodology”,
Technical paper 63RV, Washington, U.S. Census Bureaus and Bureau of Labor statistics,
March 2002. http://www.census.gov/prod/2002pubs/tp63rv.pdf
Gali, J., Gertler, M., Lopez-Salido, D., (2001). “European Inflation Dynamics”,
European Economic Review 45(7), 1237-1270.
Hubrich, K., (2003). “Forecasting euro area inflation: Does aggregating forecasts by
HICP component improve forecast accuracy?”, ECB Working Paper No 247.
Kitov, I., (2005a). "A model for microeconomic and macroeconomic development,"
Working Papers 05, ECINEQ, Society for the Study of Economic Inequality.
Kitov, I., (2005b). "Modelling the overall personal income distribution in the USA from
1994 to 2002," Working Papers 07, ECINEQ, Society for the Study of Economic Inequality.
Kitov, I., (2006a). "Inflation, Unemployment, Labor Force Change in the USA".
Working Papers 28, ECINEQ, Society for the Study of Economic Inequality.
Kitov, I., (2006b). "The Japanese economy". Available at SSRN:
http://ssrn.com/abstract=886663.
Kitov, I., (2006c). "GDP growth rate and population". Working Papers 42, ECINEQ,
Society for the Study of Economic Inequality.
Kitov, Ivan, (2006d)." Inflation, Unemployment, Labor Force Change in European
countries". (in preparation)
Mankiw, N.G., (2005). “The macroeconomist as scientist and engineer”, manuscript,
Harvard University,
http://post.economics.harvard.edu/faculty/mankiw/papers/Macroeconomist_as_Scientist.pdf
Rudd, J., Whelan, K., (2005). “New tests of the New Keynesian Phillips Curve. Journal
of Monetary Economics”, forthcoming.
Sbordone, A. (2002). “Prices and Unit Labor Cost: a New Test of Price Stickiness”.
Journal of Monetary Economics 49(2), 265-292.
Stock, J.H., Watson, M.W., (1999). "Forecasting inflation," Journal of Monetary
Economics 44, 293-335.
Stock, J.H., Watson, M.W., (2005). “Has inflation become harder to forecast?”,
manuscript, Harvard University,
http://ksghome.harvard.edu/~JStock/pdf/qepd_sw_jmcb_submission_1.pdf
23
Tables
Table 1. Results of regression analysis.
Regression Coefficient Intercept R2
Adjusted
R2
Standard
error t Stat P-value
Annual inflation /annual
dLF/LF vs. annual inflation
0.763
(0.099)
0.010
(0.005) 0.620 0.610 0.015 7.68 4.2E-09
Annual inflation /annual
dLF/LF(corrected)
0.890
(0.085)
0.004
(0.004) 0.752 0.745 0.0123 10.45 1.9E-12
Annual inflation /July-June
dLF/LF
0.847
(0.086)
0.007
(0.004) 0.727 0.720 0.013 9.80 1.1E-11
Annual inflation /annual
dLF/LF+ 1/2 year shifted LF
0.940
(0.077)
0.003
(0.004) 0.807 0.802 0.011 12.27 2.0E-14
Annual inflation /annual
dLF/LF(corrected) + 1/2 year
shifted LF
0.95
(0.077)
0.000
(0.003)
0.845 0.842 0.001 14.02 3.7E-16
Annual inflation /2 year
average dLF/LF
(corrected+1/2 year shifted)
1.08
(0.071)
-0.003
(0.003)
0.866 0.862 0.009 15.24 2.8E-14
Annual inflation /3year
average dLF/LF
(corrected+1/2 year shifted)
1.13
(0.060)
-0.004
(0.003)
0.894 0.891 0.008 17.41 4.0E-19
Annual inflation /4 year
average dLF/LF (corrected)
1.01
(0.058)
0.01 (0.0
03)
0.02 0.893 0.89 0.008 17.36 4.4E-19
2 year average inflation / 2
year average dLF/LF + 1/2
year shifted
1.05
(0.059)
-0.001
(0.002)
0.897 0.894 0.008 17.67 2.5E-19
3 year average inflation / 3
year average dLF/LF+ 1/2
year shifted
1.010
(0.042)
0.001
(0.002)
0.941 0.939 0.006 23.87 1.2E-23
4 year average inflation / 4
year average dLF/LF +1/2
year shifted
0.917
(0.030)
0.005
(0.001)
0.963 0.962 0.004 30.61 2.20E-27
Cumulative inflation /
cumulative dLF/LF
1.015
(0.004)
-0.020
(0.005) 0.999 0.0999 0.014 230.27 5.2E-60
Cumulative inflation (CPI) /
cumulative dLF/LF
1.039
(0.008)
-0.095
(0.010) 0.998 0.0998 0.026 125.06 3.2E-50
24
Table 2. Inflation forecasts for two distinct periods: between 1965 and 1983; and
between 1983 and 2002. Mean and standard deviation (same as RMSFE) are shown
for reference.
1965-2002 1965-1983 1983-2002
mean stdev mean stdev mean stdev
GDP deflator 0.043 0.024 0.060 0.023 0.027 0.009
predictor R2
stdev R2
stdev R2
stdev
1 year LF (corrected+1/2 year
shifted) 0.84 0.010 0.73 0.012 0.67 0.005
2 year average LF (corrected+1/2
year shifted) 0.87 0.009 0.79 0.011 0.65 0.005
3 year average LF (corrected+1/2
year shifted) 0.89 0.008 0.81 0.010 0.72 0.005
4 year average LF (corrected+1/2
year shifted) 0.89 0.008 0.79 0.011 0.69 0.005
25
Figures
-0.04
0.00
0.04
0.08
0.12
1940 1950 1960 1970 1980 1990 2000 2010
calendar year
inflation
GDP deflator
4*dLF(t-2)/LF(t-2))-0.03
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
1960 1970 1980 1990 2000 2010
calendar year
cu
mu
lative
inflation
GDP deflator
4*dLF(t-2)/LF(t-2))-0.03
Figure 1. Observed and predicted inflation (GDP deflator). The predicted values are obtained using
relationship (1). The upper panel compares annual readings and the lower one – cumulative values. Notice
high variation in the labor force annual increments.
26
-1000
-500
0
500
1000
1500
2000
1958
1960
1962
1964
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
calendar year
ad
justm
en
t, 1
00
0
Figure 2. Step adjustments to the levels of labor force estimates conducted by the US Bureau of Labor
Statistics between 1960 and 2004.
27
-1000
-500
0
500
1000
1500
2000
1960 1970 1980 1990 2000 2010
calendar year
co
rre
ctio
n, #
Figure 3. Corrections applied for smoothing the step adjustments in the labor force level shown in Figure 2.
The corrections proportionally distribute the adjustments over previous years.
28
-500
0
500
1000
1500
2000
2500
3000
3500
1940 1950 1960 1970 1980 1990 2000 2010
calendar year
dL
F
Original
Corrected
Figure 4. Results of the corrections to the BLS labor force estimates – comparison of the original and
corrected increments in the labor force level. A lower volatility is observed except for 1990.
29
0
2000
4000
6000
8000
1975 1980 1985 1990 1995 2000 2005
calendar year
#CB postcensal
BLS CNP
CB intercensal
Figure 5. Comparison of the annual increments in the civilian noninstitutional population reported by BLS
(CNP BLS) and the annual increments in the civilian population of 16 years of age and over as reported by
the US Census Bureau for the postcensal and intercensal estimates.
30
0
1000
2000
3000
4000
1985 1987 1989 1991 1993 1995 1997 1999
calendar year
#
original
1990 corrected
Figure 6. The labor force increments around 1990 after removing the spike in the 1990 CNP estimate.
31
0.00
0.02
0.04
0.06
0.08
0.10
0.12
1960 1970 1980 1990 2000 2010
calendar year
inflatio
n
Figure 7. Comparison of the measured inflation to that predicted using the corrected labor force estimated
and a half-year shift.
32
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
1940 1950 1960 1970 1980 1990 2000 2010
calendar year
infla
tio
n
GDP deflator
4 years
Figure 8. Comparison of the observed and predicted inflation time series smoothed by a four-year wide
moving window. The original value of the labor force in 1990 is intentionally used in order to demonstrate
the influence of the measurement errors on the otherwise excellent agreement.
33
-0.02
-0.01
0
0.01
0.02
0.03
0.04
2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
calendar year
pre
dic
ted
in
flatio
n r
ate
Figure 9. Predicted inflation rate for the period between 2006 and 2016 according to the CBO’s (2004)
labor force projection. A deflationary period starts in 2012.